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Non-equilibrium coherence dynamics in one-dimensional Bose gases

Abstract

Low-dimensional systems provide beautiful examples of many-body quantum physics1. For one-dimensional (1D) systems2, the Luttinger liquid approach3 provides insight into universal properties. Much is known of the equilibrium state, both in the weakly4,5,6,7 and strongly8,9 interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached10. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state11. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions12. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach13. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems14,15,16. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

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Figure 1: Schematic of the experiment.
Figure 2: Direct observation of the phase dynamics through interference.
Figure 3: Time evolution of the coherence factor for uncoupled 1D quasi-condensates.
Figure 4: Time evolution of the coherence factor for coupled 1D quasi-condensates.

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Acknowledgements

We thank A Burkov, V. Gritsev, E. Demler, R. Bistritzer and E. Altman for discussions. We also thank S. Groth for fabricating the atom chip used in the experiments. We acknowledge financial support from the Wittgenstein Prize and the European Union, through Atom Chips and FET/QIPC SCALA projects.

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Correspondence to J. Schmiedmayer.

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Hofferberth, S., Lesanovsky, I., Fischer, B. et al. Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007). https://doi.org/10.1038/nature06149

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